Heterogeneous Fixed Fleet Vehicle Routing Research Articles

An Approach to Solve the Heterogeneous Fixed Fleet Vehicle Routing Problem With Time Window Based on Adaptive Large Neighborhood Search Meta-Heuristic

An Approach to Solve the Heterogeneous Fixed Fleet Vehicle Routing Problem With Time Window Based on Adaptive Large Neighborhood Search Meta-Heuristic

Optimized transportation scheduling for precast concrete components considering heterogeneous vehicle-size matching

Recently, prefabricated construction has been vigorously promoted, resulting in high demand for precast concrete (PC) components. The transportation scheduling optimization problem of PC components with various kinds from multiple projects arises. Unlike conventional cargo, PC components are characterized by shape heterogeneity, large volume, and strict delivery time limits. Based on three characteristics, a heterogeneous fixed fleet vehicle routing problem (HFFVRP) for PC components is introduced, where heterogeneous vehicles, allocation of PC components to size-matching vehicles, and hybrid time windows are considered. Then a two-stage solution strategy based on the improved ant colony optimization (ACO) and Dijkstra algorithm is designed to obtain optimal vehicle routes under minimum transportation costs. The results indicate that the improved ACO-Dijkstra algorithm outperforms in obtaining optimal transportation plans for heterogeneous vehicles compared with manual decision-making and other heuristic algorithms. Sensitivity analysis denotes that utilizing heterogeneous vehicles contributes to reductions in transportation costs, and vehicle configuration should be adjusted along with demand scales. The proposed model and algorithm extend the theoretical basis of construction industrial applications.

Mathematical Model and Simulated Annealing Algorithm for the Two-Dimensional Loading Heterogeneous Fixed Fleet Vehicle Routing Problem

This paper addresses the two-dimensional loading heterogeneous fixed fleet vehicle routing problem, which is a complex and unstudied variant of the classical vehicle routing problem and has a wide range of applications in transportation and logistics fields. In this problem, each customer demands a set of rectangular two-dimensional items, and the objective is to find the minimum cost delivery routes for a limited set of vehicles with different capacities, fixed and variable operating costs, and rectangular two-dimensional loading surfaces. We formulate a mixed integer linear programming model to obtain optimal solutions for small-scale problems. To obtain solutions for large-scale problems, we develop an algorithm based on simulated annealing and local search, which uses a collection of packing heuristics to address the loading constraints, and we also propose three new heuristics. We conduct experiments on benchmark instances derived from the two-dimensional loading heterogeneous fleet vehicle routing problem. The results indicate that the proposed model correctly describes the problem and can solve small-scale problems, that the new packing heuristics are effective in improving the collection of packing heuristics, and that the proposed simulated annealing algorithm can find good solutions to large-scale problems within an acceptable computational time. Hence, it can be used by logistic companies using a heterogeneous fixed fleet in the integrated planning of vehicle loading and routing.

A Hybrid of Sine Cosine and Particle Swarm Optimization (HSPS) for Solving Heterogeneous Fixed Fleet Vehicle Routing Problem

Heterogeneous fixed fleet vehicle routing problem is a real-life variant of classical VRP, which is a well-established NP-hard optimization problem. In this paper, a hybrid approach based on sine cosine algorithm and particle swarm optimization, namely HSPS, is proposed to solve heterogeneous vehicle routing problem. This hybridization incorporates the strength of both the algorithms for solving this variant. It works in two stages. In first stage, sine cosine algorithm is used to examine the unexplored solution space, and then in next stage, particle swarm optimization is used to exploit the search space. The proposed algorithm has been tested and compared with other algorithms on several benchmark instances. The numerical and statistical results demonstrate that the proposed hybrid is competitive with other existing hybrid algorithms in solving benchmarks with faster convergence rate.

Logic-based Benders decomposition for the heterogeneous fixed fleet vehicle routing problem with time windows

This paper presents exact algorithms based on logic-based Benders decomposition and a variant, called branch-and-check, for the heterogeneous fixed fleet vehicle routing problem with time windows. The objective is to service, at the minimal cost, a set of geographically dispersed customers within their time windows by a limited and capacitated fleet of heterogeneous vehicles. The proposed algorithms decompose the problem into a generalized assignment master problem and independent traveling salesman subproblems with time windows. Valid optimality and feasibility cuts are devised to guarantee the convergence of the algorithms, which include enhancements to solve the master problem and the subproblems. Extensive computational experiments on 216 benchmark instances illustrate the effectiveness of the suggested approaches. Instances with up to 100 customers are solved to proven optimality and the results indicate that the best proposed algorithm is competitive with state-of-the-art methods.

Multiobjective mathematical models and solution approaches for heterogeneous fixed fleet vehicle routing problems

In this paper, we study three types of heterogeneous fixed fleet vehicle routing problems, which are capacitated vehicle routing problem, open vehicle routing problem and split delivery vehicle routing problem. We propose new multiobjective linear binary and mixed integer programming models for these problems, where the first objective is the minimization of a total routing and usage costs for vehicles, and the second one is the vehicle type minimization, respectively. The proposed mathematical models are all illustrated on test problems, which are investigated in two groups: small-sized problems and the large-sized ones. The small-sized test problems are first scalarized by using the weighted sum scalarization method, and then GAMS software is used to compute efficient solutions. The large-sized test problems are solved by utilizing the tabu search algorithm.

A mathematical formulation and heuristic approach for the heterogeneous fixed fleet vehicle routing problem with simultaneous pickup and delivery

<p style='text-indent:20px;'>This study considers a variant of the vehicle routing problem (VRP) called the heterogeneous VRP with simultaneous pickup and delivery (HVRPSPD). The HVRPSPD may broadly be defined as identifying the minimum cost routes and vehicle types. To solve the HVRPSPD, first, we propose a polynomial-size mixed integer programming formulation. Because the HVRPSPD is an NP-hard problem, it is difficult to determine the optimal solution in a reasonable time for moderate and large-size problem instances. Hence, we develop a hybrid metaheuristic approach based on the simulated annealing and local search algorithms called SA-LS. We conduct a computational study in three stages. First, the performance of the mathematical model and SA-LS are investigated on small and medium-size HVRPSPD instances. Second, we compare SA-LS with the constructive heuristics, nearest neighborhood and Clarke-Wright savings algorithms, adapted for the HVRPSPD. Finally, the performance of SA-LS is evaluated on the instances of the heterogeneous VRP (HVRP), which is a special case of the HVRPSPD. Computational results demonstrate that the mathematical model can solve small-size instances optimally up to 35 nodes; SA-LS provides good quality solutions for medium and large-size problems. Moreover, SA-LS is superior to simple constructive heuristics and can be a preferable solution method to solve HVRP and VRPSPD instances successfully.

A firefly algorithm for the heterogeneous fixed fleet vehicle routing problem

Vehicle routing is a key success factor in logistics problems. A variation of vehicle routing problem (VRP), the heterogeneous fixed fleet VRP in which the vehicles available for distribution activities are characterised by different capacities and costs, is tackled. A hybrid firefly algorithm for optimising the routing of heterogeneous fixed fleet of vehicles in logistics distribution systems is presented. The principles and key steps of the proposed firefly algorithm are introduced in detail. Experimental results from solving the heterogeneous fixed fleet vehicle routing problem when tested on benchmark datasets are demonstrated. Moreover, the algorithm is compared with other algorithms solving similar problems in order to prove the effectiveness of the proposed hybrid firefly algorithm.

A Firefly Algorithm for the Heterogeneous Fixed Fleet VRP

Vehicle routing is a key success factor in logistics problems. A variation of vehicle routing problem (VRP), the heterogeneous fixed fleet VRP in which the vehicles available for distribution activities are characterised by different capacities and costs, is tackled. A hybrid firefly algorithm for optimising the routing of heterogeneous fixed fleet of vehicles in logistics distribution systems is presented. The principles and key steps of the proposed firefly algorithm are introduced in detail. Experimental results from solving the heterogeneous fixed fleet vehicle routing problem when tested on benchmark datasets are demonstrated. Moreover, the algorithm is compared with other algorithms solving similar problems in order to prove the effectiveness of the proposed hybrid firefly algorithm.

Heterogeneous fixed fleet vehicle routing problem based on fuel and carbon emissions

In this paper, we study an emission-based heterogeneous fixed fleet vehicle routing problem (E-HFFVRP) with considerations of fuel and carbon emissions. This problem involves routing a fleet of a fixed number of vehicles with various capacities to serve a set of customers. It seeks to minimize the objective function, which incorporates the fixed expenses and variable costs consisting of fuel consumptions and carbon emissions. It is a new variant of the heterogeneous fixed fleet vehicle routing problem (HFFVRP), in which a fleet consists of a fixed number of vehicles with different capacities, fixed costs and variable costs. We formulate this problem with a mixed integer programming model by introducing an approach to calculate fuel and carbon emissions. Moreover, a split-based adaptive tabu search (SATS) algorithm using an optimal split scheme and an adaptive tabu search algorithm is proposed. Its key features and components are designed accordingly. Results of numerical experimentations on two sets of generated instances confirm the efficiency and effectiveness of the algorithm.

A VARIABLE NEIGHBORHOOD SEARCH FOR THE HETEROGENEOUS FIXED FLEET VEHICLE ROUTING PROBLEM

The heterogeneous fixed fleet vehicle routing problem (HFFVRP) is investigated using the variable neighborhood search (VNS). The initial solution is generated using the Sweep algorithm and the 2-opt procedure and then the customers are allocated to the smallest vehicle first by considering vehicle occupancy level. The proposed VNS algorithm uses several neighborhoods and a number of local search methods which are adapted for this problem. The local searches are implemented within a multi-level framework. The performance of the proposed algorithm is then tested using data set taken from literature and the experiments show competitive results with less computing time. Future research directions are also highlighted.

A hybrid algorithm of local search for the heterogeneous fixed fleet vehicle routing problem

Under consideration is the optimization problem for the routes of heterogeneous vehicles serving a given set of customers. It is assumed that the customers are represented by points in the plane, whereas the number of each type of vehicles is limited. To solve the problem, we developed a hybrid local search algorithm with coding the solutions as a sequence of customers. To decode the sequence, the corresponding NP-hard problem is solved by the method of Lagrangian relaxation. We propose new procedures for intensification and diversification of the search, as well as a new neighborhood of exponential size. The results of computational experiments are presented for the available test instances with the number of customers up to 255. For 15 instances we obtain new record values of the objective function.

A hybrid evolutionary algorithm for heterogeneous fleet vehicle routing problems with time windows

This paper presents a hybrid evolutionary algorithm (HEA) to solve heterogeneous fleet vehicle routing problems with time windows. There are two main types of such problems, namely the fleet size and mix vehicle routing problem with time windows (F) and the heterogeneous fixed fleet vehicle routing problem with time windows (H), where the latter, in contrast to the former, assumes a limited availability of vehicles. The main objective is to minimize the fixed vehicle cost and the distribution cost, where the latter can be defined with respect to en-route time (T) or distance (D). The proposed unified algorithm is able to solve the four variants of heterogeneous fleet routing problem, called FT, FD, HT and HD, where the last variant is new. The HEA successfully combines several metaheuristics and offers a number of new advanced efficient procedures tailored to handle the heterogeneous fleet dimension. Extensive computational experiments on benchmark instances have shown that the HEA is highly effective on FT, FD and HT. In particular, out of the 360 instances we obtained 75 new best solutions and matched 102 within reasonable computational times. New benchmark results on HD are also presented.

An improved immigration memetic algorithm for solving the heterogeneous fixed fleet vehicle routing problem

This paper deals with the heterogeneous fixed fleet vehicle routing problem (HFFVRP) which is a generalization of the classical vehicle routing problem (VRP) in the sense that the fixed fleet of vehicles is assumed to be heterogeneous. The objective of HFFVRP is to find the best fleet composition and the collection of routes such that the total costs are minimized. To address this combinatorial optimization problem, we design and implement a hybrid heuristic model integrating a genetic algorithm, a local search mechanism and an immigration strategy. Several strategies for generating the initial population of the genetic algorithm in relation with six local search heuristics are considered. An important feature of the proposed approach refers to the immigration strategy used to ensure diversification by which the level of evolution for the new immigrant individuals increases along with the evolution of the population. The proposed algorithm is tested on a set of HFFVRP benchmark instances and the preliminary results point out that our approach is an attractive and appropriate method to explore the solution space of this complex problem leading to good solutions within reasonable computational times.

A reactive adaptive memory metaheuristic for solving HFFVRP

Product distribution is one of the most important problems in supply chain management. The heterogeneous fixed fleet vehicle routing problem (HFFVRP) is a variant of VRP that aims to determine the routes for a fleet of vehicles while satisfying demand and minimizing cost. The fleet composition is fixed and it consists of various types of vehicles. These vehicles differ according to their variable cost. In this paper, a reactive adaptive memory metaheuristic was developed which made use of the Tabu Search as an improvement procedure (ReAMTS) in order to solve the HFFVRP. The method was implemented and evaluated on two sets of test problems, which are used in the literature. In addition, its performance was compared with an exact method and a set of tractable instances. The computational results demonstrated high-quality results within a reasonable time.

Optimisation of e-commerce logistics distribution system: problem modelling and exact resolution

In order to provide a decision support tool for home deliveries planning to e-commerce websites, four variants of the VRP have been combined into a single called load specific of multiple products types within heterogeneous fixed fleet vehicle routing and scheduling problem with time windows (LS-MPT-HFFVRSPTW). This problem includes constraints that can be observed in the electronic commerce environment. This paper to consider multiple types of products and vehicles, transport conditions and time windows. The main new idea is to assure compatibility between product type and vehicle type in order to satisfy required transport conditions. Mathematically this problem is formulated as a mixed integer linear programme. The formulation has been validated by tests on instances that bring the basic model of HVRPTW. New instances were built and optimal solutions have been provided by the CPLEX solver. In the future, this base of optimal solutions can be used for comparison with other approximate solutions.

Heterogeneous fixed fleet vehicle routing considering carbon emission

The paper considers heterogeneous fixed fleet vehicle routing with carbon emission to minimizing the sum of variable operation costs. A cost-benefit assessment of the value of purchasing or selling of carbon emission rights, using a mixed integer-programming model to reflect heterogeneous vehicle routing, is incorporated. Essentially, the use of a carbon market as a means of introducing more flexibility into an environmentally constrained network is considered. Tabu search algorithms are used to obtain solutions within a reasonable amount of computation time. In particular, we show the possibility that the amount of carbon emission can be reduced significantly without sacrificing the cost due to the benefit obtained from carbon trading.

Model and Heuristics for the Heterogeneous Fixed Fleet Vehicle Routing Problem with Pick-Up and Delivery

This paper discussed the heterogeneous fixed fleet vehicle routing problem with pick-up and delivery, which different type vehicles have different...

A complementary tool to enhance the effectiveness of existing methods for heterogeneous fixed fleet vehicle routing problem

The heterogeneous fixed fleet vehicle routing problem (HFFVRP) is a variant of the standard vehicle routing problem (VRP), in which the vertices have to be served using a fixed number of vehicles that could be different in size and fixed or variable costs. In this article, we propose an integer linear programming-based heuristic approach in order to solve the HFFVRP that could be used as a complementary tool to improve the performance of the existing methods of solving this problem. Computational results show the effectiveness of the proposed method.

A hybrid tabu search to solve the heterogeneous fixed fleet vehicle routing problem

One of the most significant problems of supply chain management is the distribution of products between locations. The delivery of goods from a warehouse to local customers is a critical aspect of material logistics. The Heterogeneous Fixed Fleet Vehicle Routing Problem (HFFVRP) is a variant of the Vehicle Routing Problem (VRP) that aims to provide service to a specific customer group with minimum cost using a limited number of vehicles. We assume that the number of vehicles is fixed. We must decide how to make the best use of the fixed fleet of vehicles. In this paper we describe a Tabu Search algorithm embedded in the Adaptive Memory (TSAM) procedure to solve the HFFVRP. Computational experiments indicating the performance of the algorithm concerning quality of solution and processing time are reported.